/* mpi-div.c  -  MPI functions
 * Copyright (C) 1994, 1996, 1998, 2001, 2002,
 *               2003 Free Software Foundation, Inc.
 *
 * This file is part of Libgcrypt.
 *
 * Note: This code is heavily based on the GNU MP Library.
 *	 Actually it's the same code with only minor changes in the
 *	 way the data is stored; this is to support the abstraction
 *	 of an optional secure memory allocation which may be used
 *	 to avoid revealing of sensitive data due to paging etc.
 */
#include "count_zeros.h"
#include "longlong.h"

void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);

void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
{
    int divisor_sign = divisor->sign;
    MPI temp_divisor = NULL;

    /* We need the original value of the divisor after the remainder has been
     * preliminary calculated.	We have to copy it to temporary space if it's
     * the same variable as REM.
     */
    if (rem == divisor) {
        temp_divisor = mpi_copy(divisor);
        divisor      = temp_divisor;
    }

    mpi_tdiv_r(rem, dividend, divisor);

    if (((divisor_sign ? 1 : 0) ^ (dividend->sign ? 1 : 0)) && rem->nlimbs)
        mpi_add(rem, rem, divisor);

    if (temp_divisor) mpi_free(temp_divisor);
}

void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
{
    MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
    mpi_fdiv_qr(quot, tmp, dividend, divisor);
    mpi_free(tmp);
}

void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
{
    int divisor_sign = divisor->sign;
    MPI temp_divisor = NULL;

    if (quot == divisor || rem == divisor) {
        temp_divisor = mpi_copy(divisor);
        divisor      = temp_divisor;
    }

    mpi_tdiv_qr(quot, rem, dividend, divisor);

    if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
        mpi_sub_ui(quot, quot, 1);
        mpi_add(rem, rem, divisor);
    }

    if (temp_divisor) mpi_free(temp_divisor);
}

/* If den == quot, den needs temporary storage.
 * If den == rem, den needs temporary storage.
 * If num == quot, num needs temporary storage.
 * If den has temporary storage, it can be normalized while being copied,
 *   i.e no extra storage should be allocated.
 */

void mpi_tdiv_r(MPI rem, MPI num, MPI den) { mpi_tdiv_qr(NULL, rem, num, den); }

void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
{
    mpi_ptr_t    np, dp;
    mpi_ptr_t    qp, rp;
    mpi_size_t   nsize = num->nlimbs;
    mpi_size_t   dsize = den->nlimbs;
    mpi_size_t   qsize, rsize;
    mpi_size_t   sign_remainder = num->sign;
    mpi_size_t   sign_quotient  = num->sign ^ den->sign;
    unsigned int normalization_steps;
    mpi_limb_t   q_limb;
    mpi_ptr_t    marker[5];
    int          markidx = 0;

    /* Ensure space is enough for quotient and remainder.
     * We need space for an extra limb in the remainder, because it's
     * up-shifted (normalized) below.
     */
    rsize = nsize + 1;
    mpi_resize(rem, rsize);

    qsize = rsize - dsize; /* qsize cannot be bigger than this.	*/
    if (qsize <= 0) {
        if (num != rem) {
            rem->nlimbs = num->nlimbs;
            rem->sign   = num->sign;
            MPN_COPY(rem->d, num->d, nsize);
        }
        if (quot) {
            /* This needs to follow the assignment to rem, in case the
             * numerator and quotient are the same.
             */
            quot->nlimbs = 0;
            quot->sign   = 0;
        }
        return;
    }

    if (quot) mpi_resize(quot, qsize);

    /* Read pointers here, when reallocation is finished.  */
    np = num->d;
    dp = den->d;
    rp = rem->d;

    /* Optimize division by a single-limb divisor.  */
    if (dsize == 1) {
        mpi_limb_t rlimb;
        if (quot) {
            qp    = quot->d;
            rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
            qsize -= qp[qsize - 1] == 0;
            quot->nlimbs = qsize;
            quot->sign   = sign_quotient;
        } else
            rlimb = mpihelp_mod_1(np, nsize, dp[0]);
        rp[0]       = rlimb;
        rsize       = rlimb != 0 ? 1 : 0;
        rem->nlimbs = rsize;
        rem->sign   = sign_remainder;
        return;
    }

    if (quot) {
        qp = quot->d;
        /* Make sure QP and NP point to different objects.  Otherwise the
         * numerator would be gradually overwritten by the quotient limbs.
         */
        if (qp == np) { /* Copy NP object to temporary space.  */
            np = marker[markidx++] = mpi_alloc_limb_space(nsize);
            MPN_COPY(np, qp, nsize);
        }
    } else /* Put quotient at top of remainder. */
        qp = rp + dsize;

    normalization_steps = count_leading_zeros(dp[dsize - 1]);

    /* Normalize the denominator, i.e. make its most significant bit set by
     * shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
     * numerator the same number of steps (to keep the quotient the same!).
     */
    if (normalization_steps) {
        mpi_ptr_t  tp;
        mpi_limb_t nlimb;

        /* Shift up the denominator setting the most significant bit of
         * the most significant word.  Use temporary storage not to clobber
         * the original contents of the denominator.
         */
        tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
        mpihelp_lshift(tp, dp, dsize, normalization_steps);
        dp = tp;

        /* Shift up the numerator, possibly introducing a new most
         * significant word.  Move the shifted numerator in the remainder
         * meanwhile.
         */
        nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
        if (nlimb) {
            rp[nsize] = nlimb;
            rsize     = nsize + 1;
        } else
            rsize = nsize;
    } else {
        /* The denominator is already normalized, as required.	Copy it to
         * temporary space if it overlaps with the quotient or remainder.
         */
        if (dp == rp || (quot && (dp == qp))) {
            mpi_ptr_t tp;

            tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
            MPN_COPY(tp, dp, dsize);
            dp = tp;
        }

        /* Move the numerator to the remainder.  */
        if (rp != np) MPN_COPY(rp, np, nsize);

        rsize = nsize;
    }

    q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);

    if (quot) {
        qsize = rsize - dsize;
        if (q_limb) {
            qp[qsize] = q_limb;
            qsize += 1;
        }

        quot->nlimbs = qsize;
        quot->sign   = sign_quotient;
    }

    rsize = dsize;
    MPN_NORMALIZE(rp, rsize);

    if (normalization_steps && rsize) {
        mpihelp_rshift(rp, rp, rsize, normalization_steps);
        rsize -= rp[rsize - 1] == 0 ? 1 : 0;
    }

    rem->nlimbs = rsize;
    rem->sign   = sign_remainder;
    while (markidx) {
        markidx--;
        mpi_free_limb_space(marker[markidx]);
    }
}
